Mathematical Sciences: Numerical Assessments of Goodness-of Fit Tests based on Statistically Equivalent Blocks

本研究将检验使用无分布或非参数模型建模的多变量数据的拟合优度检验。基于间隔的测试统计量的小样本行为将使用蒙特卡罗方法进行研究，并将与极限分布理论结果进行比较。通过构造统计等价块，可以将测试统计扩展到多维情况。当试图为真实的多变量数据表示一个潜在的解释性或描述性模型时，一个关键的困难是确定一个假设模型何时是足够的。最初所做的数学假设越少，一般就越难以确定模型确实代表了重要的特征，而不是特定样本的任何工件。对于任意大样本的情况，已经发展了一些数学理论；当假设数据服从高斯（正态）分布时，已经发展了一些理论。本项目将在样本不是特别大，同时分布不能假定为正态分布的情况下检查模型充分性检验。这项工作将集中在多变量观测上。

This research will examine goodness-of-fit tests for multivariate data modeled using distribution-free or nonparametric models. The small sample behavior of test statistics based on spacings will be investigated using Monte Carlo methods and will be compared to limiting distribution theoretical results. By constructing statistically equivalent blocks, test statistics can be extended to the multidimensional case. When trying to represent an underlying explanatory or descriptive model for real multivariate data, a crucial difficulty is to determine when a postulated model is adequate. The fewer the mathematical assumptions made initially, the more difficult in general to be sure that the model does represent the important features, but not any artifacts of a particular sample. Some mathematical theory has been developed for the case of an arbitrarily large sample; some theory has been developed when the data is assumed to follow a Gaussian (normal) distribution. This project will examine tests of model adequacy when the samples are not extremely large and at the same time the distribution cannot be assumed to be normal. The work will concentrate on multi- variate observations.